Video Transcript
Consider the expression three 𝑥
cubed 𝑦 over five 𝑥𝑦 divided by six 𝑥 to the power of four over five 𝑦 to the
power of four.
It is often easier to rewrite the
expression using the division symbol as follows: three 𝑥 cubed 𝑦 divided by five
𝑥𝑦 divided by six 𝑥 to the power of four divided by five 𝑦 to the power of
four. Then, we can rewrite the expression
using the multiplication symbol: three 𝑥 cubed 𝑦 divided by five 𝑥𝑦 multiplied
by five 𝑦 to the power of four divided by six 𝑥 to the power of four.
Now, use this form to help you
simplify the original expression. There are two ways of approaching
this problem. We could cancel or simplify first
and then multiply the two fractions or we could multiply the two fractions and
simplify this single fraction. We’re going to use the second
method.
Multiplying the two numerators
gives us 15𝑥 cubed 𝑦 to the power of five as three 𝑥 cubed 𝑦 multiplied by five
𝑦 to the power of four is equal to 15𝑥 cubed 𝑦 to the power of five. In the same way, multiplying the
denominators, five 𝑥𝑦 multiplied by six 𝑥 to the power of four, gives us 30𝑥 to
the power of five 𝑦.
We can then cancel or simplify this
expression. 15 divided by 30 is equal to a
half. 𝑥 cubed divided by 𝑥 to the power
of five leaves us 𝑥 squared on the denominator. And 𝑦 to the power of five divided
by 𝑦 is 𝑦 to the power of four.
Therefore, the simplified
expression is 𝑦 to the power of four divided by two 𝑥 squared. Rewriting the initial expression
has made it easier to simplify.
